PRICE-BASED SPECTRUM MANAGEMENT IN COGNITIVE RADIO NETWORKS Fan Wang, Marwan Krunz, and Shuguang Cui Department of Electrical & Computer Engineering, University of Arizona Cognitive Radio Oriented Wireless Networks and Communications, CrownCom

Outline 2  Introduction  System Model  Problem Formulation  Utility Function  Game Formulation  Optimal Pricing Function  Iterative Algorithm  Sequential & Parallel  Conclusion  Comments

Introduction 3  One of the main challenges in an opportunistic CRN  How to design an efficient and adaptive channel access scheme that supports dynamic channel selection and power/rate allocation is a distributed environment Maximize the CRN performance without disturbing PR (Primary Radio) transmissions. A typical measure of efficiency is the achievable sum-rate of all CR pairs.

Introduction (cont’d) 4  Resource allocation - Iterative water-filling [28]  A non-cooperative game was used to model the spectrum management problem with each user iteratively maximizing its own rate.  This per-user optimization problem is convex and leads to a water-filling solution. For the two-user case, it was shown that the Nash Equilibrium exists and the IWF algorithm converges to the NE under certain conditions. However, this NE is generally not Pareto optimal and may be quite inefficient in terms of the sum-rate metric. Each user tries to maximize its own utility function without considering the overall system performance. [28] W. Yu. Competition and cooperation in multi-user communication environments. Ph.D. Dissertation, Stanford University, Stanford, CA, 2002.

Introduction (cont’d) 5  A centralized spectrum management scheme [4]  Improves the system performance over the IWF scheme by utilizing a centralized spectrum management center  However, such a centralized approach cannot be implemented in a distributed ad hoc CRN  Motivation of this paper  Design a channel/power/rate allocation scheme that overcomes the inefficiency of the classic IWF algorithm can be implemented in a distributed fashion provide incentives to CR users such that they can reach a more socially efficient NE A commonly used incentive technique is pricing.

Introduction (cont’d) 6  Price-based iterative water-filling algorithm  We show that this PIWF algorithm maintains the simplicity and distributed operation of the original IWF algorithm.  A challenging problem The effectiveness of the pricing approach depends on the appropriate selection of the “pricing function”  In this paper, we use a user-dependent pricing function the sum-rate of the achieved NE after a few iterations. a pricing function can be determined by allowing each CR user to distributively explore the neighborhood information via control- packet exchanges.

System Model 7  A hybrid network  Several primary radio networks and one CRN The CRN contain N CR pairs. The total spectrum consists of K orthogonal frequency channels (K<N) with central frequencies f 1,f 2,…,f k Each CR may simultaneously transmit over multiple channels  Let M i (f k ) denote the total noise-plus-interference level measured by CR user i over channel k This quantity includes the PR-to-CR interference, the CR-to- CR interference, and the thermal noise.

System Model (cont’d) 8  This figure gives a channel allocation example for a CRN with K=3 and N=4.  Denote the set of utilized channels for CR link i as S i S 1 = {f 1,f 2 }  The transmission power vector of CR link i over various channels is denoted by P i = [P i (f 1 ), Pi(f 2 ),…,P i (f k )] P i (f k ) is the transmission power of CR i on channel k. utilized by a CR Link

System Model (cont’d) 9  Constraints  Maximum transmission power constraint The total transmission power of a CR user over the selected channels should not exceed P max   CR-to-PR power mask constraint The transmission power of CR i on channel k is constrained by P mask (f k ), which denotes the power mask associated with channel k. P mask defines as [P mask (f 1 ), P mask (f 2 ),…,P mask (f k )] Assume that P mask is given a priori.

Problem Formulation 10  A normal game can be expressed in the form  G = { Ω, P, {U i }} Ω ={1, 2, …, N} is a finite set of rational players P = P 1 x P 2 x … x P N is the action space with P i being the action set for player I U i : P  R is the utility (payoff) function of player i, which depends on the strategies of all players  Player  CR users  Actions  transmission powers  Utility  associated with their actions and the quality of the channels

Problem Formulation (cont’d) 11  Utility Function  The utility function of user i can be considered as the reward received by this user from the network. h ii (f k ): the channel gain between the transmitter and the receiver of link i over channel k M i (PR) (f k ): the PR-to-CR interference at the receiver of CR link I over channel k Ni(f k ): the received thermal noise power on channel k   Nash Equilibrium (after several iteration and under certain condition) CR-to-CR interferencePR-to-CR Noise

Problem Formulation (cont’d) 12  The resulting NE may be far from the Pareto Optimum those in which any change to make any person better off is impossible without making someone else worse off. (Wiki) w i : the weight assigned to user i  A new utility function for user i

Problem Formulation (cont’d) 13  c i (f k ): the pricing function for user i on channel k =  Our goal is to choose a user-dependent pricing function that can drive the CR users to converge to an “social- efficient” NE

Problem Formulation (cont’d) 14  Game Formulation The game in our setup can be easily shown to be a concave game if the following two properties are satisfied: 1.The action space P is a closed and bounded convex set. 2.The utility function U i (P i ) is concave over its strategy  A concave game always admits at least one Nash Equilibrium Proposition 1: For any given P max and P mask values, there is at least one NE for the game G

Problem Formulation (cont’d) 15  Optimal Pricing Function  In power control context, pricing is often used as an incentive mechanism to improve the efficiency of the NE  Fixed pricing factor for players isn’t suitable for distributed manner. One contribution of this paper: Introducing a user-dependent linear pricing function that drives the NE close to the Pareto optimal frontier with each player knowing only partial information about the networks.

Problem Formulation (cont’d) 16  Proposition 2 Consider the game G with utility function U~i, i=1…N, as defined in (3), and let the pricing function c i (f k ) be given by c i (f k ) = λ i (f k )P i (f k ). Then, the game has at least one NE solution (from proposition 1). Further, if this NE solution is Pareto optimal, then the pricing factor λ i (f k ) must be: can be proved by the Lagrange function and KKT-condition

Problem Formulation (cont’d) 17  Intuitively, a higher pricing factor λ i (f k ) will prevent user i from using a large transmission power on channel k. If a neighbor j is to transmit over channel k, it needs to broadcast its transmission power P j (f k ), the measured total noise and interference M j (f k ), and the channel gain h jj (f k ) between the transmitter and the receiver of link j. The above information can be incorporated into MAC control packets

Iterative Algorithms 18  Each CR user, say i, first adjusts its linear pricing factor λ i (f k ) over all channels, and then determines its best response The optimal channel/power/rate combination based on the measured M i The best response of user i is to maximize its individual utility function subject to the constraints C1-C3 The same procedure converges, then by definition, it has to converge to a NE of the game.

Iterative Algorithms (cont’d) 19  Proposition 3 By treating the other users’ transmissions as interference, the best response of user i is given by: the analysis provided in [23] can be extended to arrive at the result in Proposition 3. β : the water level, is determined by user i as the minimum non-negative value that results in satisfying the total power constraint C2. [23] G. Scutari, D. P. Palomar, and S. Barbarossa. Asynchronous iterative water-filling for Gaussian frequency-selective interference channels: A unified framework. Submitted to IEEE Transactions on Information Theory, August price interference channel gain transmission power

Iterative Algorithms (cont’d) 20  Sequential Price-based Iterative algorithm converge condition

Iterative Algorithms (cont’d) 21  Proposition 4 Suppose that the pricing function takes a linear form with a fixed pricing factor over a few iterations. Then, the sequential update procedure converges to the unique NE if one of the following two sets of conditions is satisfied. From above, the convergence and the uniqueness of NE are ensured if the CRs that share the same channel are far apart, and thus inflict weak interference on each other.

Iterative Algorithms (cont’d) 22  Parallel Price-based Iterative algorithm

Iterative Algorithms (cont’d) 23 Compare with the classic approachSequential vs. Parallel

Iterative Algorithms (cont’d) 24  Relaxation Algorithm  more robust to occasional estimation errors and channel oscillations at the cost of slower convergence speed Sequential algorithm’s best response Parallel algorithm’s best response A larger α (0≤ α <1) means a longer memory (less adaptation to the environment), but slower convergence As proved in [23],

Conclusions 25  Proposed two priced-based iterative water-filling algorithm that overcome the inefficiency of the classic approach.  The parallel algorithm can converge faster than the sequential one, especially for a large number of users.

Comments 26  A different approach (game theory) to solve the power control problem  Use pricing manner as the cost function to control the selfishness of CR user  Consider the overall system performance!

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